Timeline for Transfer independance from $\mathbb{N}$ to $\mathbb{N}^2$
Current License: CC BY-SA 3.0
5 events
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| Aug 19, 2011 at 10:35 | comment | added | kaleidoscop | Then I think one should look for a function $\psi$ that scatters the points somehow. I think it could be related to find Borel sets $A$ and $B$ occupying half the measure everywhere, meaning for all Borel $C$, $${\rm leb}(A\cap C)={\rm leb}(B\cap C)={\rm leb}(C)/2,$$ but I guess this is impossible. | |
| Aug 18, 2011 at 22:30 | comment | added | Noah Stein | The lemma that the entropy of a function of a discrete random variable is at most the entropy of the random variable itself is false if you replace "discrete" with "continuous" and "entropy" with "differential entropy". For example you can scale a Gaussian random variable to produce one with any given variance and thereby any differential entropy. So at least this proof does not apply to variables with density. | |
| Aug 18, 2011 at 22:08 | comment | added | kaleidoscop | Indeed, very elegant solution, thank you very much. It should also apply to variables with density, no? | |
| Aug 18, 2011 at 22:07 | vote | accept | kaleidoscop | ||
| Aug 18, 2011 at 20:33 | history | answered | Noah Stein | CC BY-SA 3.0 |